a milk container is made of metal sheet in the shape of a frustum of a cone whose volume is 10459 3/7cm cube. The radii of its lower and upper circular end are 8 centimetre and 20 centimetre. Find the cost of metal sheet used in making the container at the rate of rupee 1.40 per square cm.
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Answer:
Rs. 2462.60
Step-by-step explanation:
Upper radius (r) = 8 cm
Lower diameter (R)= 20 cm
The volume of frustum = 10459 3/7 cm³ = 10459.4285 cm³
Therefore height of frustum(h) = ?
Volume = π/3. h (R² + r² + R.r)
10459.4285 = π/3. h (20² + 8² + 160)
∴ h = 16.01 cm ≅ 16 cm
The surface area of container = π (R+r) √(R-r)² + h²
= π (20 + 8) √(12² + 16²) ≅ 1759 cm²
Cost of metal for making container = ₹ 1.4 /cm²
Cost of metal = 1.4 . 1749 = Rs. 2462.60
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